Planning, Execution and Learning Application: Examples of Planning for Mobile Manipulation and Articulated Robots

Transcription

1 Planning, Execution and Learning Application: Examples of Planning for Mobile Manipulation and Articulated Robots Maxim Likhachev Robotics Institute Carnegie Mellon University

2 Two Examples Planning for Mobile Manipulation Planning for Articulated Robots Carnegie Mellon University 2

3 Two Examples Planning for Mobile Manipulation Planning for Articulated Robots Carnegie Mellon University 3

4 Robotic Bartender Demo ([Phillips et al.]) Robot takes in a command from User Interface as to what soda can and snack to deliver Carnegie Mellon University 4

5 Typical Sequence of Operations (State Machine) Carnegie Mellon University 5

6 Typical Sequence of Operations (State Machine) How do you pick proper x,y,ѳ for picking up? Carnegie Mellon University 6

7 Typical Sequence of Operations (State Machine) ARA*-based planning on x,y,ѳ with full-body collision checking for every edge Carnegie Mellon University 7

8 Graph for Navigation with Complex 3D Body [Hornung et al., 12] 3D (x,y,θ) lattice-based graph representation for full-body collision checking takes set of motion primitives as input takes N footprints of the robot defined as polygons as input each footprint corresponds to the projection of a part of the body onto x,y plane collision checking/cost computation is done for each footprint at the corresponding projection of the 3D map Carnegie Mellon University 8

9 Graph for Navigation with Complex 3D Body [Hornung et al., 12] 3D (x,y,θ) lattice-based graph representation for full-body collision checking takes set of motion primitives as input takes N footprints of the robot defined as polygons as input each footprint corresponds to the projection of a part of the body onto x,y plane collision checking/cost computation is done for each footprint at the corresponding projection of the 3D map Carnegie Mellon University 9

10 Typical Sequence of Operations (State Machine) Running perception. Outside of the scope of this class with the exception of the next lecture Carnegie Mellon University 10

11 Typical Sequence of Operations (State Machine) Pick a primitive that approximates the object the best and use one of the grasps pre-computed for this primitive Carnegie Mellon University 11

12 Typical Sequence of Operations (State Machine) ARA*-based planning on q1, q7 towards an arm configuration that has its end-effector at the pre-grasp pose (partially-defined goal) Carnegie Mellon University 12

13 Typical Sequence of Operations (State Machine) ARA*-based planning on q1, q7 towards an arm configuration that has its end-effector at the pre-grasp pose (partially-defined goal) Or a sampling-based planner such as RRT-Connect [Kuffner & LaValle, 00] would work well (would have to plan towards a full arm configuration computed by IK) Carnegie Mellon University 13

14 ... Manipulation Lattice for Arm Planning [Cohen et al., 13] Representation ex. Single arm with n joints {θ 1,...,θ n } q 1 {θ 1,...,θ n }... q 2 {θ 1,...,θ n } q 0 {θ 1,...,θ n } q 3 {θ 1,...,θ n } Carnegie Mellon University 14

15 Manipulation Lattice for Arm Planning [Cohen et al., 13] Representation ex. Single arm with n joints {θ 1,...,θ n } Motion Primitives Static shoulder pan elbow flex Carnegie Mellon University 15

16 Manipulation Lattice for Arm Planning [Cohen et al., 13] Representation ex. Single arm with n joints {θ 1,...,θ n } Motion Primitives Static Adaptive Snap-to-goal motion Analytical solver & IK-based (only if feasible) Capable of satisfying arbitrary goal constraint despite discretization Carnegie Mellon University 16

17 Manipulation Lattice for Arm Planning [Cohen et al., 13] Non-uniform Dimensionality far from goal: only 4 DoFs active around goal: all 7 DoFs are active Non-uniform Resolution far from goal: larger discretization of joint angles around goal: finer discretization of joint angles 4D 1. Shoulder pan 2. Shoulder pitch 3. Upper arm roll 4. Elbow flex 7D 1. Shoulder pan 2. Shoulder pitch 3. Upper arm roll 4. Elbow flex 5. Forearm roll 6. Wrist flex 7. Wrist roll Carnegie Mellon University 17

18 Informative Heuristics for Arm Planning [Cohen et al., 13] Any ideas? Carnegie Mellon University 18

19 Informative Heuristics for Arm Planning [Cohen et al., 13] Euclidean distance for the end-effector? deep local minima! h Euclidean End-effector path according to heuristic large local minima many expansions Carnegie Mellon University 19

20 Informative Heuristics for Arm Planning [Cohen et al., 13] 3D BFS for end-effector accounting for obstacles computes distances from each <x,y,z> to the goal for the end-effector sphere dramatically better than Euclidean distance admissible fast to compute h BFS End-effector path according to heuristic shallow local minima fewer expansions Carnegie Mellon University 20

21 Typical Sequence of Operations (State Machine) Move the arm from pre-grasp pose towards grasp pose (computed via IK) and close the gripper Carnegie Mellon University 21

22 Typical Sequence of Operations (State Machine) ARA*-based planning on q1, q7 towards the home arm configuration (fully-defined goal) Carnegie Mellon University 22

23 Typical Sequence of Operations (State Machine) ARA*-based planning on q1, q7 towards the home arm configuration (fully-defined goal) How do you enforce upright constraints? Carnegie Mellon University 23

24 Two Examples Planning for Mobile Manipulation Planning for Articulated Robots Carnegie Mellon University 24

25 Little Dog Demo [Vernaza et al., 09] Little Dog robot needs to traverse a fully-known terrain Planning Plans footsteps first with an anytime variant of A* Compute COM of the robot afterwards to support execution Carnegie Mellon University 25

26 Footstep Planner [Vernaza et al., 09] Assumptions of the planner: Only one leg lifted at a time to ensure static stability Center of mass shifts during quadsupport phase to prevent tipping Footholds chosen deliberately to maximize stability Carnegie Mellon University 26

27 Footstep Planner [Vernaza et al., 09] Planner builds (on-the-fly/implicit) Stance Graph: Node (stance): 9-dimensional foothold configuration - feet positions and current gait phase Edge: feasible transition between stances Edge costs for transitions computed based on risk, anticipated delay Carnegie Mellon University 27

28 Implementation of GetSuccessors(s) Function Finite set of good quality candidate footholds selected prior to planning Valid stances are kinematically feasible 4-tuples of candidate footholds Successors of a given stance computed by: - determining reachable candidate footholds that result in a valid stance Carnegie Mellon University 28

29 Implementation of GetCost(s,s ) Function Edgecosts are weighted sum of: Overhead Fixed cost per step Center of mass travel Discourages backwards motion of COM Incircle radius Farthest distance from interior to exterior of support triangle Carnegie Mellon University 29

30 Implementation of GetCost(s,s ) Function Edgecosts are weighted sum of: Collision Risk of body/foot colliding with terrain Foot height variance Encourages robot to stay level Carnegie Mellon University 30

31 Implementation of GetCost(s,s ) Function Edgecosts are weighted sum of: Reachability Robot's ability to reach next foothold, switch to next support triangle without dragging feet Terrain slope Ensures terrain slope supports direction of motion Terrain cost Considers slippage potential given terrain Carnegie Mellon University 31

32 Implementation of GetCost(s,s ) Function Edgecosts are weighted sum of: Reachability Robot's ability to reach next Fine tuning foothold, them is switch not fun to next support triangle without dragging feet Terrain slope Ensures terrain slope supports direction of motion Terrain cost Considers slippage potential given terrain Lots of features make up the cost function. Carnegie Mellon University 32

33 Implementation of GetCost(s,s ) Function Edgecosts are weighted sum of: Reachability Robot's ability to reach next Fine tuning foothold, them is switch not fun to next support triangle without dragging feet Terrain slope Ensures terrain slope supports direction of motion Terrain cost Considers slippage potential given terrain Lots of features make up the cost function. Any thoughts on making the process easier? Using Learning Cost (Inverse RL) function we learned before! See it being used for LittleDog by [Zucker et al., 09] Carnegie Mellon University 33

34 Sometimes smart but often stupid no footstep planning Carnegie Mellon University 34

35 Summary Multiple planners used for both domains Start and goal configurations are often most constrained can be exploited by the planners Cost is really complex in planning for articulated robots (e.g., quadrupeds and humanoids) Planning is higher-dimensional but can take longer than on ground and aerial vehicles Design of proper heuristics is a key to efficiency Carnegie Mellon University 35